Acoustic Length Sensor for Soft Extensible Pneumatic Actuators with a Frequency Characteristics Model IROS2019国际学术会议论文集 2535

Acoustic Length Sensor for Soft Extensible Pneumatic Actuators with a Frequency Characteristics Model Ken Takaki1 Yoshitaka Taguchi1 Satoshi Nishikawa2 Ryuma Niiyama2 and Yoshihiro Kawahara1 Abstract In this study we present a length sensor that can be used for extensible soft pneumatic actuators Conventional length sensors detect the changes in electrical resistance and capacitance owing to the deformation of the actuator hence deterioration and destruction occur when they are used with an actuator that has a large expansion ratio In addition their low resolution and linearity makes them unsuitable for use in actuator control Our proposed sensor comprises only a speaker and a microphone installed at one end of the actuator We propose a method to deterministically measure the length of a tube by generating a broadband acoustic signal in a tube and measuring the resonance characteristics determined by the shape of the tube Our experimental results demonstrate that the error in the measurement with our sensor is not more than 4 with a strain up to 200 Unlike conventional acoustic sensing methods that measure the time of fl ight by using ultrasound our proposed method yields accurate results even when the tube is bent Therefore the proposed method can be applied to various types of pneumatic actuators I INTRODUCTION Soft pneumatic actuators are safer and more suitable for interaction with people owing to their softness and compliance Several robot arms equipped with soft actuators have been proposed 1 2 however precise control of these was diffi cult as the soft arms were easily deformed when subjected to an external force due to the environment In addition the materials used for soft robots are elastic and have strong nonlinear characteristics Therefore to control soft robots precisely fast and accurate length sensing is crucial Several sensors were proposed to sense the length of soft pneumatic actuators One method was to integrate a sensor inside an actuator with stretchable strain gauges However the stiffness of the sensors themselves often restricts the deformation of the actuators 3 To solve this problem em bedding microchannels fi lled with a liquid conductor inside the soft materials was suggested By adopting these methods contact and the length of the actuators could be sensed accurately and precise position control could be achieved 4 5 However there was a risk of leakage of the liquid in these sensors Stretchable sensors using optics were also developed These were free from the risk of leakage of liquid but required special materials to transmit light and some of This work was supported by JST ERATO Grant Number JPMJER1501 Japan 1School of Engineering The University of Tokyo 7 3 1 Hongo Bunkyo ku Tokyo Japan takaki kawahara akg t u tokyo ac jp ytaguchi ginjo t u tokyo ac jp 2Graduate School of Information Science and Technology The Uni versity of Tokyo 7 3 1 Hongo Bunkyo ku Tokyo Japan nisikawa niiyama isi imi i u tokyo ac jp Signal Processing Microcontroller Length Pressure Control Speaker Microphone Airport Air Column Length Change Freq Chirp Signal Freq Response Time a System with the proposed length sensor The pressure applied to the actuator is controlled on the basis of the length calculated by the sensor 100 mm microcontroller unit speaker microphone 28 mm 12 mm b The proposed sensor is attached to the left end of the extensible pneumatic actuator Fig 1 Structure of the proposed length sensor and its use them required additional expensive equipment for precision measurement 6 7 Finally wrapping conductive yarns around the actuators was suggested however the linearity of the sensor value and repeatability are sacrifi ced 8 9 All the sensors mentioned above have a limited range of sensing up to a strain of 100 and embedding them in existing actuators is quite expensive In this study we propose a high dynamic range 200 strain length sensor consisting of a tiny speaker and a microphone attached to one end of the tube of a soft pneu matic actuator as shown in Fig 1 The speaker generates a chirp signal inside the tube of the actuator which causes resonance inside the tube By recording the resonance with a microphone and analyzing it it is possible to determine the length of the tube deterministically In previous studies acoustic properties were used to measure the length of a pipe 10 12 One technique was to use the Time of Flight ToF where the distance was derived from ultrasonic pulses and their refl ections from objects The precision of this method is limited by parasitic refl ection which is attributed to surface ripples The use of longer wavelengths resolved this problem 10 However this process requires a large speaker to generate the low frequency signal making it impossible to apply it to the column in soft actuators In addition it is vulnerable to the infl uence of deformation Methods based on the measurement of frequency charac IEEE Robotics and Automation Letters RAL paper presented at the 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 Copyright 2019 IEEE teristics 11 12 were suggested These methods could measure the lengths of pipes accurately however the time required for recording and analyzing was approximately one second which is not suitable for real time control of actuators that move dynamically To overcome this drawback we adopted a parametric method by which the frequency characteristics are ascer tained rapidly and accurately using minimal computing re sources available even on simple microcontrollers With this method it becomes possible to measure the length of an extensible pneumatic actuator with a strain up to 200 and an error of 4 and more quickly than previous methods we are able to achieve a response time of 90ms The main contributions of this study are as follows 1 We established a sensing method based on acoustic resonance to measure the length of a soft pneumatic actuator accurately and rapidly 2 We incorporated the proposed sensing method into a continuum arm and demonstrated that the arm could distinguish between grasped objects of different sizes The remaining part of this paper is structured as follows The principle of the proposed length sensor is described in Section II An evaluation of the performance of the sensor based on experiments is described in Section III The length control of a soft actuator using the proposed sensor and its performance are discussed in Section III B A soft robot arm made of bundled soft actuators with our sensor is introduced and the grasping interactions are explained in Section III C The limitations and further possibilities of this work are discussed in Section IV The outcome of the study is discussed in Section V II WORKING PRINCIPLE AND SENSOR IMPLEMENTATION A Acoustics inside Pneumatic Actuators We modeled the acoustics inside the Extensible Pneumatic Actuator with Bellows EPAB 13 and compared with the measured results EPAB is a cylindrical actuator that extends axially when air is supplied As shown in Fig 2 the resonance frequency interval between the peaks differs for different lengths of the actuator and there are slight differ ences between the peak frequencies of the model and those in the measurement We fi rst discuss the simple acoustic model inside the actuator Let the length of the centerline of the actuator be L the inner radius of the rubber tube inside the actuator be r the speed of sound be c zero of the Bessel function be 1 8412 and the nth resonant frequency be fn n 0 1 2 Under the assumption that the speaker is not affected by the environment the acoustics inside the actuator can be modeled according to Eq 1 11 14 Only plane waves propagate when the frequency is lower than the specifi c frequency given by Eq 1 and the equation holds good even when the actuator is curved If f is equal to fn 1 fn then from Eq 1 the length of the actuator can 020004000600080001000012000 160 140 120 100 80 frequency shift peak elimination a Frequency response when the length is 265mm 020004000600080001000012000 160 140 120 100 80 region used for length estimation 3 kHz to 12 kHz b Frequency response when the length is 390mm Fig 2 Frequency response inside the pneumatic actuator when the length is 265mm and 390mm with different pressures inside the air column be written as Eq 2 fn cn 2L fn c 2 r 1 L c 2 f 2 We now discuss the application of the above model to soft pneumatic actuators Normally a speaker generates sound by moving the surrounding air by a vibrating diaphragm Acoustic resonance occurs as a result of interaction between the speaker air under pressure and the wall of the column cavity The diffi culty arises when mode coupling between the speaker and the air column of the actuator under high pressure causes a shift or an elimination of the specifi c resonant frequency as shown in Fig 2 a Both the cavity and speaker have an intrinsic resonance mode and the coupling between them is weak when no pressure is applied to the cavity However as the air pressure in the cavity increases cross interaction between the cavity and speaker becomes prominent If the air pressure in the cavity becomes even higher the mode coupling becomes weak again Mode cou pling occurs in this situation causing a shift in the resonant frequency at specifi c frequency bands Further details and effects of mode coupling are discussed in 15 The effect of mode coupling does not impose any limitation on the available pressure range of the proposed sensor To overcome this diffi culty it is necessary to measure the resonance characteristics in a wide frequency band and deduce f from the band that is not affected by the mode coupling as shown in Section II C B Length Sensor and Controller Design The design of the proposed length sensor and controller is discussed in this section As shown in Fig 1 a length control is achieved by regulating the pressure applied to the actuator on the basis of the calculated length The length sensor consists of a balanced armature speaker Knowles SR6438NWS 000 and transmits a signal into the air column of the actuator At the same time the electret condenser microphone CUI CMC 4015 40P records the refl ected sound which depends on the length of the actuator At least two adjacent resonances must be excited to calculate the length of the actuator from Eq 2 for which a signal with a broadband spectrum must be injected In this study the radius of the rubber tube of the actuator was 6mm thus according to Eq 1 the maximum frequency is approximately 16 7kHz We determined by means of experiments that a frequency range from 3kHz to 12kHz was suffi cient for our actuator therefore we used a 5ms chirp signal which sweeps from 0Hz to 12kHz It is important to start from 0Hz to prevent distortion of the signal The interval of chirps determines the refresh rate of the length sensor the shorter the interval the faster the refresh rate of the length sensor However the interval must be long enough to allow the chirp to decay fully as well as provide enough time for the calculation of length to be completed Therefore the interval between the chirps should be selected by recording the sound inside the actuator for various lengths and measuring its reverberation time In this experiment 10ms was suffi cient for the signal to attenuate Next amicrocontroller STMicroelectronics STM32L432KCU6 was used to process the recorded sound to calculate the length The algorithm is described in detail in Section II C The calculated length is sent to the length controller via an I2C bus The assembled sensor with all the components is shown in Fig 1 b The proposed sensor is 12mm in diameter and its length is 28mm It can be installed into the actuator by merely inserting it into one side of the air column The controller with a microcontroller STMicroelectronics STM32F767VIT6 regulates the pressure valve based on the calculated length received Further details about the controller are given in Section III B C Signal Processing In this section the methods of calculating the resonant frequencies inside the air column of EPAB are discussed We performed a system identifi cation of the air column First a broadband acoustic signal was provided by the speaker The system recorded the sound using the microphone and analyzed the frequency characteristics of the EPAB column Harmonics were observed in the recorded signal due to resonance The length of the actuator was calculated by using Eq 2 and the value of f obtained from the peaks observed in Fig 2 One naive approach is by using the Fourier transform and analyzing the signal in the frequency domain However our preliminary experiments showed that it was diffi cult to achieve an improvement in the accuracy as well as a reduction in delay in the measurement when the Fourier transform is used The reason is that the resolution of frequency of the Fourier transform is determined by the recording time number of samples To improve the accuracy of measurement more samples must be taken which also 30003500400045005000 140 120 100 80 60 Fig 3 Frequency response measured with different signals and algorithms 10 ms FFT fails to locate the peak near 4kHz whereas the peaks of the envelope by 10 ms LPC successfully match the true peaks increases the delay in measurement The mutual dependence between the resolution of frequency and recording time is due to the mathematical properties of the Fourier transform Let f be fn 1 fn f be the resolution of f and L be the resolution of length L As an example one second of the recorded sound results in f 1Hz and if the resonant frequency f is f 1000Hz f 1Hz results in L 1 7mm Although the resolution of the length is high the sensing procedure is very slow On the other hand if we consider 10ms of the recorded sound to make the sensing procedure faster f is 100Hz When f 1000Hz f 100Hz results in L 170mm This L is too coarse to be used for length sensing To overcome the above problems we adopted parametric methods for detection of the resonant frequency The fre quency resolution of this type of algorithm is not bounded by the recording time 16 Thus the problem of interde pendence of resolution of frequency and recording time due to the Fourier transform is resolved We used the linear prediction coeffi cients LPC algorithm to determine the spectral envelope This algorithm is lightweight enough to be executed on microcontrollers 17 The LPC algorithm approximates signals under the as sumption that the signal can be expressed in the form of a linear differential equation As the acoustics inside the air column can be expressed in the form of a linear differential equation LPC is suitable for approximating the signal The Levinson Durbin algorithm 18 is suitable for the determination of the spectral envelope which is a continuous function Therefore the frequency resolution by this method is not affected by the number of samples unlike the FFT method As shown in Fig 3 when the number of samples is insuffi cient the resolution is low in the analysis by FFT whereas by using LPC the envelope can be smoothly obtained with a lesser number of samples To determine the peak frequencies we split the frequency spectrum into several sections and applied the golden search algorithm to each We rejected the frequency peaks that were insignifi cant in terms of signal amplitude as such peaks are strongly affected by the mode coupling mentioned in Section II A We calculated the frequency gaps between the peaks rejecting the outliers based on the median of all the gaps and averaged these to calculate the value of f given in Eq 2 The process of averaging is important as it takes into account the frequency gaps that are both larger and smaller than the ideal frequency making the calculated frequency gap close to the ideal one Finally the length was calculated by using Eq 2 The time taken for processing all the above on a microcon troller that was currently used for the sensor see Section II B was 80ms However as 10ms is long enough for the interval between the chirps a measurement rate of 100Hz is possible by replacing the microcontroller On the other hand in a previous study a parametric method used to measure the length of a pipe 11 took 1 3s on a Laptop computer with 400MHz of CPU which is much slower than our method III EXPERIMENTS A Sensor Evaluation The accuracy of the proposed length sensor is evaluated in this section First we determined the effect of a load applied to the sensor on the accuracy of the measured length This assessment was conducted by using the following setup We fi xed one end of the actuator to a load cell NIDEC SHIMPO FGP 100 and the other end to an elevating stage We attached a rotary encoder MUTOH INDUSTRIES D 1000Z C to the stage to measure the ground truth length Then we slowly extended the actuator from 220mm to 600mm by moving the stage at the rate of 30mm min and controlled the pressure inside the actuator to maintain the applied load Fig 4 shows the calculated length of the slowly moving actuator with applied loads of 10N and 40N and the results of the estimation of length with and without fi ltering the peak outliers are compared The calculated length roughly agreed with the ground truth length through the entire region and when a load of 10N was applied to the actuator the results were an root mean square error RMSE of 14 9mm and root mean square percentage error RMSPE of 4 0 with peak fi ltering an RMSE of 105 0mm and RMSPE of 37 3 without peak fi ltering When a load of 40N was applied the results were an RMSE of 17 2mm and RMSPE of 3 9 with peak fi ltering an RMSE of 94 0mm and RMSPE of 30 0 without peak fi ltering Although the calculated length generally agreed with the ground truth length under different loads there was a difference in the regions where the errors were relatively large This occurred because the pressure applied to the actuator differs under different loads The effect of pr